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A Dynamic Generalization of the Rasch Model

Published online by Cambridge University Press:  01 January 2025

N. D. Verhelst  and
C. A. W. Glas
N. D. Verhelst*
Affiliation:
National Institute of Educational Measurement (CITO), Arnhem, The Netherlands
C. A. W. Glas
Affiliation:
National Institute of Educational Measurement (CITO), Arnhem, The Netherlands
*
Requests for reprints should be sent to N. D. Verhelst, Cito PO Box 1034, 6801 MG Arnhem, THE NETHERLANDS.
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Abstract

In the present paper a model for describing dynamic processes is constructed by combining the common Rasch model with the concept of structurally incomplete designs. This is accomplished by mapping each item on a collection of virtual items, one of which is assumed to be presented to the respondent dependent on the preceding responses and/or the feedback obtained. It is shown that, in the case of subject control, no unique conditional maximum likelihood (CML) estimates exist, whereas marginal maximum likelihood (MML) proves a suitable estimation procedure. A hierarchical family of dynamic models is presented, and it is shown how to test special cases against more general ones. Furthermore, it is shown that the model presented is a generalization of a class of mathematical learning models, known as Luce's beta-model.

Keywords

Rasch modelmissing dataincomplete designsdynamic modelsmathematical learning theory

Information

Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 395 - 415
Copyright
Copyright © 1993 The Psychometric Society

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